Nonlocal elliptic problems in infinite cylinder and applications

Nonlocal Elliptic Boundary Value Problems

On Elliptic Boundary Value Problems in the Complement of an Infinite Cylinder

A boundary value problem for certain elliptic operators in the comple ment of an in nite cylinder is studied We prove that for these operators P D with some general zero boundary conditions if P D u has support inside a cylinder and decays exponentially in one direction of the cylinder then the solution u under a certain strong radiation condition at in nity must have support inside the cylinde...

RCS of Chiral Elliptic Cylinder Embedded in Infinite Chiral Medium

Received Jan 29, 2017 Revised Jun 10, 2017 Accepted Aug 11, 2017 This paper presents an analytic solution to the scattering properties of chiral elliptic cylinder embedded in infinite chiral medium due to incident plane wave. The external electromagnetic fields as well as the internal electromagnetic fields are written in terms Mathieu functions and expansion coefficients. In order to obtain bo...

Generalized Solutions of Nonlocal Elliptic Problems

An elliptic equation of order 2m with general nonlocal boundary-value conditions, in a plane bounded domain G with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space Wm 2 (G) are studied. The Fredholm property of the unbounded operator corresponding to the elliptic equation, acting on L2(G), and defined for functions from the space Wm 2 (G) that satis...

On a Class of Nonlocal Elliptic Problems with Critical Growth

This paper is concerned with the existence of positive solutions to the class of nonlocal boundary value problems of the Kirchhoff type − [ M (∫ Ω |∇u|2 dx )] Δu = λ f (x,u)+u in Ω,u(x) > 0 in Ω and u = 0 on ∂Ω, where Ω ⊂ RN , for N=1,2 and 3, is a bounded smooth domain, M and f are continuous functions and λ is a positive parameter. Our approach is based on the variational method.